Abstract—In this paper, a modelling approach for a
photovoltaic solar cell has been proposed which begins with the
development of a solar cell up to enabling the solar cell to be
implemented at circuit level simulations. This modelling
approach is useful in the photovoltaic field to have an initial or
overall observation on the effects toward the photovoltaic
system. The modelling approach begins with modelling a thin
film Cu(In,Ga)Se2 (CIGS) solar cell using Silvaco TCAD
(Technology Computer-Aided Design) software with a
predefined baseline parameters. The electrical parameters as
well as the I-V curve of the TCAD model are obtained and the
data is exported to be post-processed in Matlab software. Key
parameters of the TCAD model are used to develop an
equivalent electrical model. The Single-diode model topology is
implemented for simplicity. In order to test the validity of the
single-diode model, the I-V curve is compared to the I-V curve
of the TCAD model. As an extension, the I-V curves are also
presented across different temperatures in order to test the
accuracy of the single-diode model
Keywords—modelling, photovoltaic, solar cell, circuit level,
TCAD, Matlab, I-V curve, single-diode
I. INTRODUCTION
Solar energy is a popular and emerging renewable energy
source due to the theoretically infinite resource from the
sun. Besides, there are no moving parts involved in the
conversion of solar energy to electrical energy which makes
it almost maintenance free. Solar energy is associated with
the term photovoltaic (PV) which covers the conversion of
solar energy into electrical energy using semiconductor
materials known as the solar cell. Typically, an isolated,
stand-alone, or off-grid PV system consists of three main
components such as the solar module, the charge controller
module, and the battery system. The solar module is a group
of solar cells connected together to achieve a higher solar
energy output. The charge controller module is where
Maximum Power Point Tracking (MPPT) algorithm is
implemented, and the battery system is to store the
converted solar energy for later usage.
It can be observed that there are several areas available
for research, such as the solar cell, the MPPT algorithm, and
the power management of the battery system. The solar cell
is the first component of the PV system where the sun’s
irradiance is taken as the input to be converted into electrical
energy. The maximum output power is directly proportional
to the efficiency of the solar cell. Thus, there are abundance
of researches done to develop solar cells that are capable of
converting solar energy to electrical energy at a higher
efficiency. This includes developing solar cells from
different kinds of materials and processes [1]. Besides the
solar cell, there are also significant researches done on the
MPPT algorithm to be implemented in the PV system. The
objective is to ensure the PV system operates at the
Maximum Power Point (MPP) of the solar cell by
continuously tracking the MPP. There are continuous
researches done to improve the conventional algorithm such
as the Perturb and Observe (P&O) algorithm [1]. Besides,
there are also new algorithms with higher complexity being
introduced such as the fuzzy logic approach and the grey
wolf algorithm [3], [4]. The battery system is another
section in the PV system where till date, there are researches
done to implement new or improve currently available
power management systems [5], [6].
A modelling approach for PV solar cell which is a
combination of Silvaco TCAD and Matlab software is
proposed. The modelling approach begins with defining the
baseline parameters of the solar cell. The resulting electrical
characteristics and the non-linear I-V curve of the solar cell
will be used to develop an equivalent electrical model of the
solar cell. The validity of the model is tested at different
temperatures such as 280K, 300K, and 320K. The electrical model is used to provide an initial insight
on the performance of the solar cell when implemented in a PV system. This includes the impact towards the PV system when changes are made to the baseline parameters of the solar cells. This is significant in the PV field as the performance of a solar cell can be observed as a single cell or as a whole PV system.
II. DESCRIPTION OF THE MODELLING APPROACH
Solar cell device development and solar PV system are
usually developed separately. During the solar cell device
development, the baseline parameters of the solar cell are
manipulated to improve the efficiency and electrical
characteristics of the solar cell. For example, to improve the
efficiency of a thin film CIGS solar cell, the thickness,
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doping concentration, electron affinity, and band gap energy
are manipulated [7]. The results of the changes are discussed
and concluded at the solar cell level.
For the latter, solar PV system includes development of
the MPPT algorithms and the power management system.
MPPT algorithms are usually developed and tested with a
solar cell or solar module with commercially available data
[2]. This is also similar on the development of PV power
management systems where commercially available data of
the solar cell or solar module are implemented [5].
In the proposed modeling approach, a new step is
introduced to link between the solar cell device development
and the solar PV system. It is the implementation of the
solar cell as a part of a complete PV system. At this point,
the solar cell can be implemented in the development of the
MPPT algorithms as well as the power management system.
With this approach, the flexibility of the PV simulation flow
will improve in terms of the capability to manipulate the
baseline parameters of the subjected solar cell.
III. SIMULATION OF SOLAR CELL USING SILVACO TCAD
SOFTWARE
For the modelling approach, a CIGS solar cell is designed
using Silvaco TCAD based on a predefined baseline
parameters. These parameters such as shown in Table 1 are
chosen to model an optimal thin-film CIGS solar cell based
on results of prior researchers [8], [9], and [10].
TABLE 1. PREDEFINED BASELINE PARAMETERS FOR CIGS
SOLAR CELL
Parameters Layers
ZnO CdS CIGS
Thickness (nm) 150 50 3000
Band gap, (eV) 3.3 2.4 1.27
Donor concentration, (cm-3) 1x1018 1x1017 0
Acceptor concentration, (cm-3) 0 0 2x1016
Conduction band effective
density of states, (cm-3) 2.2x1018 2.2x1018 2.2x1018
Valence band effective density of
states, (cm-3) 1.8x1019 1.8x1019 1.8x1019
Fig. 1 shows the designed TCAD solar cell model with
the baseline parameters described in Table 1. The structure
of the TCAD model is composed of Molybdenum (Mo)
back contact, a p-type wide-band gap absorber layer (CIGS),
followed by n-type buffer layer made of cadmium sulphide
(CdS) and a window layer made of doped zinc oxide (ZnO).
Fig. 1. TCAD model structure designed with Silvaco TCAD
The I-V curve of the designed solar cell at standard test
condition (STC) usually at 300 K and 1000 W/m2 and air
mass 1.5 (AM 1.5) is depicted in Fig. 2. From the I-V curve,
short-circuit current (Isc), open-circuit voltage (Voc), current
at MPP (Imp), and voltage at MPP (Vmp) is 40.3 mA, 0.752
V, 36.3 mA, and 0.649 V respectively.
These parameters will be used to develop an equivalent
electrical model of the TCAD model in the next step of this
modelling approach using Matlab software. Besides the I-V
curve, a logfile of the TCAD model is available as the
output of Silvaco TCAD. The logfile containing electrical
parameters of the TCAD model can be exported into comma
separated values (csv) file by utilizing TonyPlot (Silvaco’s
interactive visualization tool) for post-processing with other
software, which is described in the next section of this
paper.
Fig. 2. I-V curve of the TCAD model designed with Silvaco TCAD
IV. MODELLING OF THE SOLAR CELL USING MATLAB
SOFTWARE
The main purpose of using Matlab software is to construct an equivalent electrical model of the TCAD model, which is to reproduce the non-linear I-V curve. In a standard non-linear I-V curve, three marked points are highlighted such as the short-circuit (0, Isc), MPP (Vmp, Imp), and open-circuit (Voc, 0) as shown in Fig. 3.
Fig. 3. Standard non-linear I-V curve with the three marked points
Previous PV system studies have utilized different circuit topologies to represent solar cells such as the single-diode model, two-diode model, and three-diode model [11]-[13]. In this work, the single-diode model circuit topology is chosen because the model offers good compromise between simplicity and accuracy [11]. Fig. 4 shows the electrical circuit of a practical single-diode solar cell with the equivalent series and parallel resistance.
µm
µm
(0, 0.0403)
(0.649, 0.0363)
(0.752, 0)
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Ipv Id
Rs
Rp
I
V
Fig. 4. Electrical circuit representation of a practical single-diode solar cell
The I-V characteristics of a practical single-diode solar
cell is mathematically described as below [14].
(1)
where: Ipv = PV current
Io = Diode reverse saturation current
Vt = Thermal voltage
α = Diode ideality constant
Rs = Equivalent series resistance
Rp = Equivalent parallel resistance
From equation (1), the thermal voltage, Vt = kT/q where
k is the Boltzmann constant (1.3806503×10-23 J/K), T is the
temperature in Kelvin, and q is the electron charge
(1.60217646×10-19 C). The PV current, Ipv depends on the
solar irradiation and the temperature of the solar cell where
it is described as shown below [15].
(2)
where: Ipv,n = PV current at STC
KI = Short-circuit current temperature
coefficient
ΔT = Difference between actual and nominal
temperature
G = Irradiation
Gn = Irradiation at STC
Io on the other hand, is further elaborated as in equation (3)
[15].
(3)
where: Isc,n = Short-circuit current at STC
Voc,n = Open-circuit voltage at STC
KV = Open-circuit voltage temperature
coefficient
Equations (1) – (3) are used to develop the single-diode
model. The key parameters of the TCAD model are
implemented such as Isc,n, Voc,n, Imp, and Vmp. The
temperature coefficients, KI and KV are taken from the
average of commercially available CIGS solar cells
datasheet [16]-[20]. The values of the equivalent resistances
Rs and Rp are obtained through Newton-Raphson iteration
method [11]. Fig. 5 shows the reconstructed I-V curve of the
single-diode model based on the I-V curve of the TCAD
model at STC.
Fig. 5. I-V curve of single-diode model and I-V curve of TCAD model
From Fig. 5, it can be observed that the single-diode model can reconstruct the I-V curve of the TCAD model with great accuracy. This observation validates the I-V curve of the single-diode model to that of the TCAD model. The curves are exactly matched at the three marked points denoted by the dots since these points are used as the basis in developing the single-diode model. Slight error gaps are observed at other points of the I-V curve. This is the limitation of the single-diode model, although the error gaps can be reduced by increasing the number of iterations in finding the values of Rs and Rp.
V. VALIDATING THE SINGLE-DIODE MODEL AT DIFFERENT
TEMPERATURES
To further validate the I-V curve of the single-diode model, a set of I-V curves of the single-diode model and TCAD model are plotted at different temperatures. This is to ensure the single-diode model is able to accurately represent the TCAD model for further usage in the PV system. Fig. 6 shows the I-V curves of the single-diode model and the I-V curves of the TCAD model at three different temperatures such as 280K, 300K, and 320K.
Fig. 6. I-V curves of the single-diode model and TCAD model at different
temperatures
As shown in Fig. 6, the I-V curves of the single-diode
model and TCAD model are denoted by the dotted line and
solid line respectively. The different temperatures are
denoted by the colors and numbers where blue (1) is for
------ Single-diode model
------ TCAD model
o Marked points
….... Single-diode model
____ TCAD model
(1) 280K (2) 300K
(3) 320K (3)
(1)
(2)
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280K, black (2) is for 300K, and red (3) is for 320K. The
absolute error between the I-V curves are as described in
Table 2.
TABLE 2. ABSOLUTE ERROR BETWEEN SINGLE-DIODE MODEL
AND TCAD MODEL AT DIFFERENT TEMPERATURES
Temperature 280K 320K
Voc Isc Voc Isc
Single-Diode Model
(a)
0.807V 38 mA 0.696 V 41 mA
TCAD Model (b) 0.790V 41 mA 0.710 V 40 mA
Absolute Error gap
(|[a-b]/b × 100|)
2.15% 7.32% 1.97 % 2.50 %
The I-V curves are almost accurate at temperature 300K. However, when the temperature is increased or decreased to 320K and 280K respectively, the absolute error between the I-V curves increases. From Table 2, it can be observed that the single-diode model is able to maintain at most an absolute error of 7.32% which is at 280K. This result indicates that the single-diode model is sufficiently accurate to the TCAD model at temperature ranging from 280K to 320K. This is significant in implying the validity of the single-diode model to replace the TCAD model for circuit level simulations.
VI. CONCLUSION & DISCUSSION
In this paper, a modelling approach has been proposed to
be implemented in PV systems. The approach is an
extension of the conventional modelling approach for solar
cells by introducing another step which enables circuit
implementation of the solar cell. This is significant in the
PV field since the approach is able to provide initial or
overall insight on how the baseline parameters of a solar cell
affects the performance of the PV system.
The modelling approach is a combination of Silvaco
TCAD and Matlab software where Silvaco TCAD is used to
develop a TCAD model of a thin-film CIGS solar cell from
a predefined baseline parameters and Matlab software is
used to post-process the output file. Matlab software is also
used to develop an equivalent single-diode model to
represent the TCAD model. The I-V curve of the single-
diode model is validated against the I-V curve of the TCAD
model at three different temperatures such as 280K, 300K,
and 320K. At most, the absolute error between the curves is
at 7.32%. This modelling approach is not only limited to model and
simulate thin-film solar cells. As long as there are information on the electrical characteristics and the I-V curve of a solar cell, this modelling approach can be utilized to develop an equivalent electrical model for circuit level simulations.
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2018 IEEE International Conference on Semiconductor Electronics (ICSE)
